The relaxation time of a reversible Markov chain \(X\)  is \(\tau _2(X) := 1/(1-\lambda _2)\) , where \(\lambda _2\)  is the second largest eigenvalue of the transition matrix. If \(X\)  is also lazy, then the \(L^2\)  contraction property (Lemma 3.26 of [1]}) states that
\(\Vert {\mathbb {P}}(X_t \in \cdot )-\pi \Vert _2 \le e^{-t/\tau _2}\Vert {\mathbb {P}}(X_0 \in \cdot )-\pi \Vert _2.\) 
